Problem: Calculate the product below and give your answer in scientific notation. $ {\left(95 \right) \times \left(3\times 10^{4} \right) =\ ?} $
Answer: First, let's change the first factor into scientific notation. $(95) \times (3.0\times 10^{4}) = (9.5\times 10^{1}) \times (3.0\times 10^{4}) $ Start by collecting the significands and exponents. $ ({9.5} \times {10^{1}}) \times ({3.0} \times {10^{4}}) = ({9.5} \times {3.0}) \times ({10^{1}} \times {10^{4}}) $ Then multiply each term separately. When multiplying exponents with the same base, add the powers together. $= {28.5} \times {10^{1 \,+\, 4}}$ $= {28.5} \times {10^{5}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the left without changing the value of our answer. We can use the fact that ${28.5}$ is the same as ${2.85 \times 10}$ or ${2.85 \times 10^{1}}$. $ = {2.85 \times 10^{1}} \times {10^{5}} $ $ = 2.85 \times 10^{{1} + {5}} $ $= 2.85\times 10^{6}$